A sample of \(6\times 10^5\)  \(W\)  jets were simulated with momenta in the range \(500 \, \text{--} \, 600 \; \text{GeV}\)  using a standard pipeline of Madgraph [1]}, Pythia8 [2]}, and Delphes [3]}. The simulated jets typically contain \(\mathcal {O}(100)\)  particles, and the 50 largest-momentum particles are selected and stored as 3-vectors \((p_T, \eta , \phi )\) , with zero-padding used for jets with fewer particles. The momenta are prescaled so that their sum is one for each jet. Two VAEs with identical architecture are trained: VAE_uncent and VAE_cent are trained on jets which have not been centered in the detector and jets that have been centered (\(\eta = \phi = 0\) ), respectively.
